The condenser quasicentral modulus

2021/09/16 by Dan-Virgil Voiculescu, Voiculescu, Dan-Virgil · 1 citation
Mathematics · #47L20 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Primary: 46L89 #Secondary: 31C45 #math.FA #math.OA #msc:31C45 #msc:46L89 #msc:47L20

paper · pdf · doi:10.48550/arxiv.2109.07633

26 pages. added sections 7 and 8 and made the necessary additions to the introduction and abstract. Minor corrections. Further addition to section 8.Further addition to section 3. Typos corrected

arxiv created 2022/08/14 · arxiv updated 2022/08/16

Abstract

We introduced the quasicentral modulus to study normed ideal perturbations of operators. It is a limit of condenser quasicentral moduli in view of a recently noticed analogy with capacity in nonlinear potential theory. We prove here some basic properties of the condenser quasicentral modulus and compute a simple example. We also discuss some associated variational problems. Part of the results are in the more general setting of a semifinite von Neumann algebra.

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